Simple atom interferometer in a double-well potential

We present a detailed study of an atom interferometer which can be realized in a double-well potential. We assume that the interferometric phase is imprinted in the presence of coherent tunneling between the wells. We calculate the ultimate bounds for the estimation sensitivity and show how they relate to the precision of the Mach-Zehnder interferometer. The interferometer presented here allows for sub shot-noise sensitivity when fed with the spin-squeezed states with reduced either the relative population imbalance or the relative phase. We also calculate the precision of the estimation from the population imbalance and show that it overcomes the shot-noise level when the entangled squeezed-states are used at the input.